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Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing various regularity properties such as metric regularity, i.e., the openness with a linear rate around the reference point, of a~(set-valued) mapping. We derive an analogue of it guaranteeing the almost openness with a linear rate of mappings acting in incomplete spaces and having non-closed graphs, in general. The main tool used is an approximate version of Ekeland's variational principle for a function that is not necessarily lower semi-continuous and is defined on an abstract (possibly incomplete) space. Further, we focus on the stability of this property under additive single-valued and set-valued perturbations., Comment: 23 pages

Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing metric regularity of a (set-valued) mapping. First, we demonstrate that one should always use directly the so-called general criterion which follows, for example, from Ekeland's variational principle, and that there is no need to make a detour through the slope-based consequences of this general statement. Second, we argue that when proving perturbation stability results, in the spirit of Lyusternik-Graves theorem, there is no need to employ the concept of a lower semi-continuous envelope even in the case of an incomplete target space. The gist is to use the "correct" function to which Ekeland's variational principle is applied; namely, the distance function to the graph of the set-valued mapping under consideration. This approach originates in the notion of graphical regularity introduced by L. Thibault, which is equivalent to the property of metric regularity. Our criteria cover also both metric subregularity and metric semiregularity, which are weaker properties obtained by fixing one of the points in the definition of metric regularity., Comment: 24 pages

Studujeme různé druhy regularity, včetně subregularity a semiregularity, mnohoznačných zobrazení mezi zobecněnými kvazimetrickými prostory. Ukážeme, že tyto abstraktní prostory umožňují sjednocení standardních vlastností regularity, jejich směrových a také Hölderovských verzí. Kritéria jsou odvozena z obecného Ekelandova principu. Výsledky jsou detailně odvozeny a rozšiřují existující teorii. Stručně nastíníme význam teoretických vět pro aplikace. Například studujeme lokální konvergenci směrové verze metod Newtonova typu pro řešení tzv. zobecněných rovnic v případě, že zobrazení nespňuje vlastnosti běžná (všesměrové lokální) regularity. We study various regularity properties, including subregularity and semiregularity, of set-valued mappings acting in extended quasi-metric spaces. It turns out that this abstract framework allows to unify criteria for the usual (sub/semi) regularity as well as their directional and Hölder counterparts. Ioffe-type critera are obtained by applying a general version of the Ekeland’s variational principle. We provide a self-contained material gathering and extending the existing theory on the topic. We (briefly) illustrate the importance of these criteria for applications. For example, we consider local convergence of a directional version of a Newton-type method for solving a generalized equation which may be applied when the usual (non-directional) regularity does not hold.

Přestože silná metrická subregularita mnohoznačných zobrazení se objevuje v literatuře pod různými názvy a různými (ekvivalentními) definicemi již více než dvacet let, nebylo jí věnováno tolik pozornosti jako metrické regularitě a silné metrické regularitě. Účelem článku je ukázat, že mnoho vlastností silné metrické subregularity je totožných s předchozími populárnějšími vlastnostmi a má mnoho praktických aplikací. Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various (equivalent) definitions for more than two decades, it has attracted much less attention than its older “siblings”, the metric regularity and the strong (metric) regularity. The purpose of this paper is to show that the strong metric subregularity shares the main features of these two most popular regularity properties and is not less instrumental in applications.

International audience; The paper is devoted to the study of the Aubin/Lipschitz-like property and the isolated calmness of a particular non-monotone generalized equation arising in electronics. The variational and non-smooth analysis is applied in the theory of non-regular electrical circuits involving electronic devices like ideal diodes, practical diodes, DIACs, silicon controlled rectifiers (SCR), and transistors. We also discuss the relationship of our results to the ones using classical techniques from (smooth) analysis and provide a simulation for several simple electrical circuits which are chosen in order to cover the most common non-smooth elements in electronics. The simulations of the electrical circuits discussed in this paper are performed by using Xcos (a component of Scilab).

The development of novel methodologies and synthetic strategies for the preparation of complex 3D heterocyclic compounds with the well-defined spatial arrangement of functional groups represents one of the most studied research problems in current synthetic chemistry. Nowadays, organocatalysis (beside transition-metal catalysis and biocatalysis) became the most popular tool, because of usage small chiral organic compound for asymmetric induction and acceleration of reaction. In this thesis, the development of novel organocatalytic methodologies for the preparation of various heterocyclic compounds is described. The utility of novel methodologies is demonstrated by easy access to chiral building block molecules or products with valuable physical or biological properties. In the first part, a novel [4+2] cycloaddition reaction of sulfur-containing heterocyclic electron-deficient alkenes with allenic compounds catalyzed by chiral tertiary amine is described. Organocatalytic cycloaddition reaction of 3-benzylidene benzo[b]thiophenones with allenoates was investigated and optimized. Dihydro-2H-pyranes were obtained in high isolated yields (up to 92%) and optical purities (up to 99% ee). The robustness and synthetic utility of the developed methodology was demonstrated by a simple work-up of...

Influenza is an infectious disease caused by the influenza virus. This virus causes a severe viral infection that spreads easily from person to person in yearly pandemics. Vaccination is the most effective way to prevent the infection, however, due to the high rate in mutations of the virus, the vaccine needs to be often reformulated. Another option to combat influenza is based on administration of antiviral drugs. Clinical studies of isolated influenza strains ("avian flu" H5N1, 2004; "swine flu" H1N1, 2009) revealed resistance towards known influenza neuraminidase inhibitors (zanamivir, oseltamivir). The resistance is caused by structural changes close to the enzymatic site. This calls for the development of new neuraminidase inhibitors as well for development of inhibitors targeting different influenza enzymes. This Thesis is focused on design and synthesis of new inhibitors of influenza neuraminidase and RNA-dependent RNA polymerase, namely PA subunit and the assembly of PA-PB1 heterodimer enzymes (Scheme 1). Influenza neuraminidase inhibitors were prepared by C-5 derivatization of oseltamivir followed by subsequent extension of its structure with binders of 150-cavity. Binding potencies of new oseltamivir derivatives against two influenza strains were determined. The next part contributed to...

2,2'-Bipyridines and their appropriate N,N'-dioxides form a significant class of heteroaromatic compounds, which has found application in various fields of chemistry and predominantly in asymmetric catalysis. One of the most powerful methods for their synthesis is cocyclotrimerization of alkynes with nitriles. A new variant of cyclotrimerization reaction - cocyclotrimerization of halodiynes with nitriles, which results in the formation of 2- and 3-halopyridines, has been developed. The reaction was studied on a wide range of substrates providing the pyridine products in good isolated yields. Formation of an unexpected product of halogen exchange reaction was observed during the course of the study and its origin was elucidated by experimental studies. The prepared 2-halopyridines were used as starting materials for syntheses of new chiral 2,2'-bipyridine ligands. The crucial step of their synthesis turned out to be the reductive dimerization of 2-halopyridines to the corresponding 2,2'-bipyridines. Application of the formed bipyridine ligands was then tested in various metal-catalyzed asymmetric reactions, namely Mukaiyama aldol reaction, hydroxymethylation, conjugate addition, C-H activation of indole and desymmetrization of meso-epoxides, in which one of the bipyridine ligands showed...

Ultrafast dynamics of phenolic and adamantyl compounds was studied by measuring time- resolved absorption changes using transient absorption spectroscopy technique (TA). Phenolic and adamantyl compounds used were adamantyl-phenol, BODIPY- phenol, naphtol and adamantyl-naphtol. Probe pulse spectrum was supercontinuum generated in calcium- fluoride (CaF2) window pumped by 800 nm or 400 nm. In the case of pumping with 400 nm white light spectrum shifted more towards UV but is inherently more unstable because the second harmonic (400 nm) is less stable than fundamental (800nm) by itself. Pump beam was frequency doubled and prism compressed output of the NOPA. NOPA output gave wavelength variability in the range 500-700 nm which was then compressed by chirped mirrors and frequency doubled in BBO crystal which resulted in wavelength variability in the range 260-300 nm. After prism compressing the pump pulse, durations of sub 20 fs were obtained which roughly defined the resolution of the measurement. Measurements were performed at 1kHz repetition rate with pump pulse energies at around 100 nJ. All of the samples undergo photochemical reaction of quinone methide generation after excitation in UV at around 275 nm. Significance of the product molecules is that quinone methides alkylate and cross-link DNA strands, which underpins the antiproliferative activity of some antitumor antibiotics. BODIPY- phenol is interesting because it does not undergo any photochemical reaction when excited into its S1 state (500 nm) but it does undergo a quinone methide generation reaction when excited into its S3 state (276 nm). At last we wanted to investigate the difference in the dynamics of naphtol and adamantyl-naphtol samples. All of the reactions are reversible, i.e. quinone methides transfer back to its initial molecules after some time so the samples are preserved but required to be flown because the lifetime of quinone methides is comparable to laser’s repetition rate so by flowing the sample we ensure that every pump pulse gets absorbed by unexcited (‘fresh’) part of the sample and we are avoiding multiple excitations. Currently, partial quantum chemical TD-DFT simulations of the photochemical reaction of the adamantylphenol are available as calculations are still in progress. Simulations of the reactions of the other 3 samples are still yet to be done. Goal of the TA measurements of the first sample was to investigate which reaction pathway do molecules take as adamantyl- phenols can undergo a reaction in which products (quinone methides) are generated in its excited state then relaxed to its ground state and transferred back to its initial molecules or initial molecules can take a reaction pathway which includes conical intersection by which products are generated immediately in their ground state in which case TA measurements show one transient state less, etc. Spectral dynamics of the first sample was quantitatively investigated and the results show fast dynamics at around 800 fs which will be assigned to one of the reaction pathways after TD-DFT quantum chemical calculations are finished. Other 3 samples were qualitatively investigated, spectral dynamics and time dynamics is shown and compared. Due to ultrashort pump pulses (very large intensity at the focus) coherent artifacts of the TA method, such as cross-phase modulation and two-photon absorption were present and largely interfered with the global analysis which had to be done to have a complete description of the photochemistry of adamantyl-phenol. Extraction and smoothening of coherent artifacts is currently being done which will greatly help with the global analysis and time dynamics analysis such as fitting the exponential decay at a certain wavelength and obtaining decay rates.

The pentafluorosulfanyl (SF5) group displays remarkable and unique properties, including large dipole moment, high electronegativity, high thermal and chemical stability, as well as high lipophilicity. However, only a few synthetic methods for the preparation of aromatic pentafluorosulfanyl building blocks have been developed to date. This work aims at improving availability and accessibility of aryl sulfurpentafluoride building blocks. In the first part of the work, the synthesis of aryl sulfurpentafluorides by the direct fluorination of diaryl disulfides with elemental fluorine is described. Nowadays, this synthetic strategy is used by industry on a multi-kilogram scale. However, the scope of the reaction is only limited to 3- and 4- nitro-1-(pentafluorosulfanyl)benzenes. In this work, the synthesis of various para-, meta- and ortho-substituted-(pentafluorosulfanyl)benzenes following the same approach was carried out. In the second part, the derivatization of aryl sulfurpentafluoride building blocks was investigated. Direct fluorination of 3-nitro-1-(pentafluorosulfanyl)benzene afforded 3-fluoro-5-nitro-1- (pentafluorosulfanyl)benzene. The titled compound was derivatized by two different processes: nucleophilic aromatic substitution (SNAr) of fluorine and vicarious nucleophilic substitution of...

The current methodologies of catalytic enantioselective allylation of aldehydes were studied on conjugated dienals and later on haloacrylaldehydes as the substrates. The resulting enantioenriched homoallylalcohols were prepared by reactions promoted either by commercial Brønsted acid catalysts or by Lewis base catalysts developed by our group, often with high enantio- and diastereoselectivities. Subsequently, the methodology was expanded on catalytic enantioselective crotylation and pentenylation reactions, practically unknown not only with these substrates. The applicability of this synthetic approach was demonstrated on preparation of several natural products or their intermediates.

Influenza viruses cause respiratory illnesses which can vary in severity depending on the strain of the virus, as well as the age and health condition of the host. Influenza remains a major threat to public health due to its nature prone to suffer mutations. As a result, vaccines have to be reformulated annually and new strains may cause sporadic global pandemics. Furthermore, the recent emergence of resistant strains of the virus against the current standard of care (oseltamivir and zanamivir) underlines the need of novel anti-influenza therapeutics. The aim of this dissertation work is to contribute to the discovery of new anti-influenza inhibitors either by rational drug-design and optimization of oseltamivir structure, or by developing screening assays suitable for the discovery of novel inhibitors of the enzymes neuraminidase or RNA-polymerase. Scheme 1. Overview of the strategy used for the development of new anti-influenza therapeutics. The dashed arrows indicate the inhibitors that were converted into probes and their corresponding target enzymes Two main modification points were explored for the improvement of oseltamivir properties (Scheme 1); modifications at carbon C-3 aimed to overcome oseltamivir resistance caused by common mutations like H274Y, meanwhile modifications at carbon C-5...

In the present thesis, both the published and the "ready-to-be-submitted" results concerning electrochemistry of calixarenes are summarized. The main focus is given to the detailed interpretation of experimental data, acquired during a systematic study of electroactive calixarene derivatives. The experiments were conducted under aprotic conditions (DMF) on mercury electrodes (mainly cyclic voltammetry and DC-polarography). It is demonstrated that electrochemistry should not serve only for redox characterization of studied compounds, but it offers a great number of other valuable information. The subject matter of the study are the calix[4]arenes (prevalently in the cone-conformation) which bear one to four reducible or oxidizable substituents ("redox probes") at various positions in order to be electrochemically investigable. Nitro- and nitroso compounds together with aldehydes, ketones, nitriles, aldoximes, carboxylic acids and corresponding esters, sulphones and esters of sulphonic acids are the most discussed compound series. Their relationship between structure and electrochemical response is presented in new connections ("stereoelectrochemistry"), in other words, how the redox probe position on the benzene ring (para-/meta-), bridging groups, or adjacent vs. opposite aromatic units...

This thesis describes the development of new thermal and oxidative radical cyclization methodologies and their application to the total syntheses of alkaloids, particularly to bridged diketopiperazine (DKP) alkaloids. A practical solvent free approach to diverse DKPs and quinazolines is described. The methodology proceeds by thermal silica gel mediated deprotection of the Boc protecting group and intramolecular condensation of the resulting free dipeptides and tripeptides. It was applied to the total syntheses of alkaloids glyantrypine and ardeemin. A major part of the thesis concerns with the discovery and applications of novel diketopiperazine derived alkoxyamines. Their propensity to undergo facile thermal C-O bond homolysis to generate captodative DKP radicals and persistent TEMPO radical allowed using them as radical surrogates. The methodology takes advantage of the persistent radical effect (PRE). The methodology based on PRE was applied in an asymmetric approach to the alkaloid asperparaline C. An asymmetric synthesis of a very advanced precursor to asperparaline C, 8- oxoasperparaline C, was accomplished in 11 steps and 15% overall yield. The key steps of the synthesis include a direct oxidative cyclization of DKPs, regioselective furan dearomatization with singlet oxygen and a reductive...

Since 2000 the organocatalytic synthesis has developed massively in a third pillar of asymmetric synthesis standing next to catalysis with metal complexes and enzymatic catalysis. Organocatalysts, due to their various activation modes which could be combined in domino reactions, offer a way for a synthesis of complex molecules from a simple starting material. This thesis deals with investigation of usage of chiral secondary amines as catalysts for asymmetric synthesis of cyclic compounds. The main part of research was devoted to development of organocatalytic method leading to synthesis of enantiomerically pure cyclopentanecarbaldehydes and nitrocyclopentanecarbaldehydes. We focused also on the organocatalytic preparation of cyclohexanecarbaldehydes. During this work we developed an asymmetric domino Michael addition/α- substitution reaction of 2-(2-bromoethyl)malonates resp. 1-bromo-3-nitropropane with various enals catalyzed by chiral secondary amine. In the first case cyclopentanecarbaldehydes were formed where two chiral centres were created. In second case nitrocyclopentanecarbaldehydes were formed where three chiral centres were created. Yields of such developed reaction protocol reach up to 74 % and the reaction proceeds with excellent diastereo- and enantioselectivity (up to 19:1 d.r. and...

New Carbanion Rearrangement of Sulfur Compounds and Its Application Abstract This thesis reports the investigation of an unusual reversal in the metalation selectivity of alkyl aryl sulfones and sulfoxides and its application. Such compounds undergo initial directed ortho-metalation at −78 řC despite having an acidic α-hydrogen atom and the resulting aryllithiums rearrange subsequently completely to the initially expected α-sulfonyllithiums on warming. The scope and the limitations for this process were identified. Both carbanion types of sulfones were applied in reactions with various electrophiles. α-Lithiated sulfones generated upon the transmetalation process were used in Julia olefinations. A mechanistic study of the course of the transmetalation reaction is presented. The kinetics of the transmetalation were determined. Investigations concerning the concentration dependence, proton transfer equilibria between the different ortho-sulfonyllithium intermediates and crossover experiments provided the evidence that a concerted intermolecular pathway prevails. On this basis a new integrated synthetic approach to naturally occurring iridoids was developed. It is based on a tandem alkoxycarbonylation/oxidative radical cyclization of the olefins synthesized by the Julia reaction after the investigated...

In this diploma thesis a detailed investigation of the step-by-step reduction mechanism of cone-mono-, di-, tri and tetranitrocalix[4]arenes (in non-aqueous DMF) is presented. The intramolecular interaction of reducible (and reduced) centers and its consequences for the geometry of the starting molecule was discussed including the character of radicalic intermediates and their spin state. It was found, that the electrochemically generated radical anions of nitrogroups (unlike their starting electroneutral state) can act as ligands. Therefore, a study of complex formation equilibria of cone-tetranitrocalix[4]arenes with alkali metal cations followed. The possible use of a "stereoelectrochemical" approach (the relationship between geometry or conformation of the molecule and its electrochemical data) was demonstrated in describing and explaining conformational and electrochemical differences between two isomeric dinitrocalix[4]arenes. Finally, a new series of 1,3-alt-tetranitrothiacalix[4]arenes was electrochemically characterized and compared with the "classic" calixarene derivatives. Key words: electrochemistry, calixarenes, stereochemistry